Zero modes in the light-front coupled-cluster method

Chabysheva, Sophia S.; Hiller, John R.

doi:10.1016/j.aop.2013.10.016

Cited by 9 publications

(8 citation statements)

References 48 publications

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“…Zero modes can be included in the LFCC method [118]. The vacuum must then also be computed as a nontrivial eigenstate, which takes the form of a generalized coherent state of zero modes [64,119].…”

Section: Light-front Coupled-cluster Methodsmentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, φ 4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

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Section: Light-front Coupled-cluster Methodsmentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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“…This approach has been applied to a light-front analog of the Greenberg-Schweber model [4,8], where the lowest-order T produces the exact answer, and to QED [7], in a calculation of the dressed-electron state and its anomalous magnetic moment. In addition, a technique for including zero modes has been developed [9] and applied to φ 3 and φ 4 theories and to the Wick-Cutkosky model. Much of this work is less briefly summarized in various proceedings [10][11][12].…”

Section: Overview Of the Methodsmentioning

confidence: 99%

A nonperturbative coupled-cluster method for quantum field theories

Hiller

2013

AIP Conference Proceedings

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The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponentialoperator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from many-body coupled-cluster theory, to obtain form factors and other observables.

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“…However, the original development of the LFCC method did not explicitly include the zero momentum modes needed for representation of a nontrivial light-front vacuum. Here we summarize recent work that rectifies this deficiency [2].…”

Section: Introductionmentioning

confidence: 99%

“…Z maintains the normalization. The eigenvalue problem can then be rewritten as 2) with P − ≡ e −T P − e T an effective Hamiltonian. We project the eigenvalue problem onto the valence and orthogonal sectors 3) with P v the projection onto the valence sector.…”

Section: Introductionmentioning

confidence: 99%